FAQ

He built the machine himself as a birthday present for his adopted son, Sherman.

The other Penny is still in ancient Egypt. In timeline A, Penny A and Sherman A travel to Egypt where she stays in order to get married to King Tut. Sherman A travels back to timeline A after he (and Penny A) used the WABAC machine. Sherman A and Peabody A travel back to Egypt in order to rescue Penny A, which they successfully do, and travel through different time periods. After Peabody A mysteriously vanishes during the Trojan War, Sherman A and Penny A go back to the timeline in which they already existed thus creating timeline B. So, the Peabody and Sherman in timeline B are now Peabody B and Sherman B, thus Penny B is still in Egypt. Suddenly, Sherman B and Peabody A (who survived the fall) return to timeline B, and a time paradox is created when the two Shermans and Peabodys merge. Despite that Sherman and Peabody fixed the paradox and established the timeline in its rightful place, Penny B is still left in ancient Egypt.